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P45841A©2016 Pearson Education Ltd.
1/1/1/1/1/
*P45841A0124*
Mathematics APaper 3H
Higher Tier
Thursday 26 May 2016 – MorningTime: 2 hours
4MA0/3HKMA0/3H
You must have:
Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions
• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name,
centre number and candidate number.• Answer all questions.• Without sufficient working, correct answers may be awarded no marks.• Answer the questions in the spaces provided
– there may be more space than you need.• Calculators may be used.
• You must NOT write anything on the formulae page.Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100.• The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.• Check your answers if you have time at the end.
Pearson Edexcel Certificate
Pearson Edexcel
International GCSE
2
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International GCSE MATHEMATICSFORMULAE SHEET – HIGHER TIER
r
Pythagoras’ Volume of cone =
Curved surface area of cone =Theorem
a2 + b2 = c2
b
a
c
adj = hyp cosopp = hyp sinopp = adj tan
or
opptanadj
adjcoshyp
oppsinhyp
a
a
Sine rule:
Cosine rule:
Area of triangle
sin Ab
+
sin Bc
sin C
opp
A B
C
b a
c
adj
hyp
Area of a trapezium = (a + b)h12
h1 2
2 b2 c 2bc
ab sin C
cos A2
3
b
a
h
a
h
b
Volume of prism = area of cross section length
lengthsectioncross
Volume of cylinder = r2h
Curved surface area
The Quadratic EquationThe solutions of axwhere a
x b b 4ac2a
0, are given bybx c 0,+
+
+
of cylinder = 2 rh
h
r
Circumference of circle = 2
Area of circle = r2
2
2
r
r 4 33
12
r
2r
Volume of sphere =
r
r
hl
l Surface area of sphere =
In any triangle ABC
4
r
3
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Answer ALL TWENTY TWO questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1 Here are the ingredients needed to make 12 muffins.
Ingredients to make 12 muffins
300g flour
150g sugar
250ml milk
100g butter
2 eggs
Sarah makes 60 muffins.
(a) Work out how much sugar she uses.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g(2)
James makes some muffins.He uses 625 ml of milk.
(b) How many muffins did he make?
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 1 is 4 marks)
4
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2 ac
(a) Work out the value of 2a2 + 6c
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
There are 4 pens in a small box of pens.There are 10 pens in a large box of pens.
Ami buys x small boxes of pens and y large boxes of pens.She buys a total of T pens.
(b) Write down a formula for T in terms of x and y.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 2 is 5 marks)
5
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3 The table shows information about the number of visits each of 40 adults made to the gym last week.
Number of visits to the gym Frequency
0 4
1 3
2 12
3 5
4 8
5 5
6 2
7 1
Work out the mean of the number of visits to the gym.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 3 is 3 marks)
4 A = {2, 4, 6, 8, 10, 12, 14} B = {1, 3, 5, 7, 9, 11, 13} C = {3, 6, 9, 12}
(a) List the members of the set
(i) A C
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) A C
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(2)
(b) Explain why A B = Ø
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 4 is 3 marks)
6
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5 On the grid, draw the graph of y = 3x – 5 for values of x
6
5
4
3
2
1
O–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
–11
–12
–2 –1 1 2 3 4
y
x
(Total for Question 5 is 4 marks)
7
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6 (a) Show that 310
215
1330
+ =
(2)
(b) Show that 2 58
116
2 14
÷ =
(3)
(Total for Question 6 is 5 marks)
8
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7 (a) Factorise 3y2 + 2y
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(1)
(b) Expand and simplify (x – 9)(x + 2)
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(2)
(c) (i) Solve 6k + 5 < 20
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) n is an integer and 6n + 5 < 20
Write down the largest possible value of n
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(d) Simplify fully 284
5 3
2x yxy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 7 is 8 marks)
9
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8 A
C
B
13.4 cm53°
Diagram NOT accurately drawn
Work out the length of AB.Give your answer correct to 1 decimal place.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question 8 is 3 marks)
10
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9 Bhavin, Max and Imran share 6000 rupees in the ratios 2 : 3 : 7
Imran then gives 35
of his share of the money to Bhavin.
What percentage of the 6000 rupees does Bhavin now have?Give your answer correct to the nearest whole number.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %
(Total for Question 9 is 5 marks)
11
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10 The diagram shows a circle inside a rectangle.
2.5 cm
13.8 cm
7.6 cm
Diagram NOT accurately drawn
Work out the area of the shaded region.Give your answer correct to 3 significant figures.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 10 is 3 marks)
12
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11 The frequency table shows information about the weights of 80 adults.
Weight (w kg) Frequency
40 < w 50 4
50 < w 60 7
60 < w 70 21
70 < w 80 21
80 < w 90 18
90 < w 100 7
100 < w 110 2
(a) Complete the cumulative frequency table.
Weight (w kg) Cumulative frequency
40 < w 50 4
40 < w 60
40 < w 70
40 < w 80
40 < w 90
40 < w 100
40 < w 110(1)
13
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(b) On the grid, draw a cumulative frequency graph for your table.(2)
40 50 60 70 80 90 100 110
Cumulative frequency
Weight (w kg)
80
70
60
50
40
30
20
10
0
(c) Use your graph to find an estimate for the number of adults with weight more than 85 kg.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(d) Use your graph to find an estimate for the interquartile range of the weights of theadults.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg(2)
(Total for Question 11 is 7 marks)
14
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12 Solve the simultaneous equations 4x + 5y = 133x – 2y = 27
Show clear algebraic working.
x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
y = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 is 4 marks)
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13 The straight line L
Find an equation of the line that is parallel to LGive your answer in the form ax + by = c where a, b and c are integers.
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(Total for Question 13 is 5 marks)
16
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14 A particle is moving along a straight line.The fixed point O lies on this line.The displacement of the particle from O at time t seconds is s metres where
s = 2t3 – 12t2 + 7t
(a) Find an expression for the velocity, v m/s, of the particle at time t seconds.
v = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Find the time at which the acceleration of the particle is instantaneously zero.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . seconds(2)
(Total for Question 14 is 4 marks)
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15 The diagram shows two mathematically similar vases, A and B.
A B
Diagram NOT accurately drawn
Vase A has a surface area of 120 cm2
Vase B has a surface area of 750 cm2 and a volume of 1600 cm3
Work out the volume of vase A.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3
(Total for Question 15 is 3 marks)
18
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16 ABCDEFGH is a cuboid.
Diagram NOT accurately drawn
A
E
G
C
H
F
D
B8 cm
5 cm
17 cm
The cuboid haslength 17 cmwidth 5 cmheight 8 cm
Work out the size of the angle that AH makes with the plane EFGH.Give your answer correct to 1 decimal place.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 16 is 4 marks)
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17 The diagram shows a trapezium.
x + 6
x – 1
3x – 4
Diagram NOT accurately drawn
All measurements on the diagram are in centimetres.
The area of the trapezium is 119 cm2
(i) Show that 2x2 – x – 120 = 0
(ii) Find the value of x.Show your working clearly.
x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 is 6 marks)
20
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18 Make t the subject of the formula m = tt
+−13
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(Total for Question 18 is 4 marks)
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19
Diagram NOT accurately drawn
A
B
C
D 75°
27°
O
A, B, C and D are points on a circle, centre O.
Angle DAB = 75° Angle DBC = 27°
Work out the size of angle ODC.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 19 is 4 marks)
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20 A metal cube has sides of length 4.5cm, correct to the nearest 0.5cm.
The cube is melted down and the metal is used to make small spheres. Each sphere has a radius of 3mm, correct to the nearest millimetre.
Work out the greatest number of spheres that could be made from the metal. Show your working clearly.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 is 5 marks)
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21 There are 9 counters in a bag. There is a number on each counter.
1 1 2 2 2 3 3 3 3
Kal takes at random 3 counters from the bag.
He adds together the numbers on the 3 counters to get his Total.
Work out the probability that his Total is 6
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 is 5 marks)
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22 The diagram shows a pentagon.
12 cm 12 cm
8 cm 8 cm
13 cm
105° 105°
Diagram NOT accurately drawn
Work out the area of the pentagon. Give your answer correct to 3 significant figures.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 22 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
